Claude Finishes a "Nine-Loop" Theoretical Physics Calculation, at $1,000 to $2,000 per Method
Anthropic has published a case study in which Claude solved a difficult theoretical physics calculation. It did not invent a new method. A human kept telling it to keep going, and it ran an existing method to completion. Running a single method is estimated to cost $1,000 to $2,000.
On September 25, Anthropic published an account of how Claude worked through a hard calculation in theoretical particle physics. The write-up came from Matt von Hippel, a science writer and former physicist. The team completed a “nine-loop” calculation, not in a theory that describes real-world particles, but in a model theory used as a testbed for calculation methods.
The calculation works out the likelihood that particles interact in a particular way. A loop is a unit that measures how complicated the interactions included in the calculation are. The more loops you include, the more precise the result, but the amount of computation needed grows along with it. For the theory in question here, N=4 supersymmetric Yang-Mills theory, results had previously been worked out up to eight loops.
What the humans actually did in the nine-loop run
Anthropic physicists Liam Fitzpatrick and Siddharth Mishra-Sharma used Fable 5.1 inside Claude Science, a paid service built for scientists. Claude Science is a version of Claude preloaded with research-oriented rules and instructions to support scientific work. The two handed it a nine-loop calculation involving six particles, then kept issuing instructions to continue the work.
Claude ran the calculation two different ways. One approach applied, one after another, the conditions the answer had to satisfy, narrowing down the candidates. The other was an indirect route that borrowed results from a separate but connected calculation. The team verified the results together with Lance Dixon of SLAC National Accelerator Laboratory, who had worked on the earlier eight-loop calculation.
What one run cost
Running each method yourself is estimated to cost between $1,000 and $2,000. Most of that is the usage fee for keeping Claude running for long stretches. In the method that narrows down the answer by applying conditions, computing the actual numbers and expressions took 96 CPUs running for a week. That computation accounted for roughly $100 of the total. In other words, when you use AI in research, you have to budget not just for compute hardware but for AI usage fees as well.
So is this a new physics discovery?
Around the same time, a team led by Song He at the Chinese Academy of Sciences obtained a substantial portion of the same results. That team got some help from GPT-6, but worked differently from Anthropic. Von Hippel’s assessment is that Claude did not invent a new calculation method. Rather, it achieved the result by pouring more computational resources into already known methods than previous attempts had.
The significance of this case lies in the fact that AI pushed a well-defined research calculation all the way to the finish line with minimal human intervention. It also offers a gauge for how far research AI can be taken and what it costs. It should be distinguished, though, from a result that directly illuminates real-world particle phenomena. Dixon, Song He, and other researchers plan to publish an explanation and analysis of the results. What to watch next is the detailed verification of the calculation and whether other researchers can reproduce the same results.